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Velocity and Speed
Introduction ---- Velocity and speed have distinct different meanings. Velocity-a vector quantity which refers to "the rate at which an object changes its position." Velocity is the rate of change in displacement with respect to time. Since displacement is a vector quantity, then velocity is also a vector quantity. It has both magnitude and direction. (A vector is a quantity which is fully described by both a magnitude and a direction.) Speed-a scalar quantity which refers to "how fast an object is moving." Speed is the rate of change in distance with respect to time. Since speed is built from distance, a scalar quantity, then speed is also a scalar quantity. This means it carries no direction information with it. (A scalar is a quantity which is fully described by a magnitude alone.) To understand the difference between speed and velocity we must understand the difference between distance and displacement. Basic Forumlas ---- Average Speed= Distance Traveled/Time Traveled Average Velocity= Change in Position/Time Traveled= Displacement/Time Traveled (v=d/t) (Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.) Average Speed vs Instantaneous Speed ---- Instantaneous Speed - speed at any given instant in time. Average Speed - average of all instantaneous speeds; found simply by a distance/time Average Speed vs Instantaneous Speed Animation Quiz ---- 1)You are driving to Mexico to visit your Grandmas to eat her scrumpcious snickerdoodle cookies. In 5 hours you drove 1000 meters to stop for milk. You still had 940 more meters to go. If you got to grandmas house in a total of 8 hours what is your average velocity between your milk rest and grandmas. 2)A car travels 90. meters due north in 15 seconds. Then the car turns around and travels 40. meters due south in 5.0 seconds. What is the magnitude of the average velocity of the car during this 20.-second interval? A)2.5 m/s B)5.0 m/s C)6.5 m/s D)7.5 m/s''''' 3)The position of an object is +35 meters at 2.0 seconds and is +87 meters at 15 seconds. Calculate the average velocity of the object. Solutions ---- 1) Position vs Time Hopefully your graph is nicer... but I really tried hard First we must convert to hours to seconds because the formula requires that we use seconds. Since we only want the average velocity between point D1 (5 Hours) and D2 (8 Hours) we must find how much time elapsed between those two places which is 3 hours. So first we multiply 3(hours)*60(Minutes per hour)*60(seconds per minute)= 1080(s). We also must find the total distance traveled between those two points which is given (940 m). We can now go ahead and use the equation. v=d/t v=940m/1080s= .870 m/s. (positive direction) Quite slow.. but then again I made the problem up. 2)(A) The basic equation is v = d/t. The DISPLACEMENT of the car is 90 m - 40 m = 50 m, the total time is 20s. V = 50m/20s 3)v=d/t. 87m-35m/15s-2s= 52m/13s= +4.0m/s The object is traveling in the positive direction with an average speed of 4.0m/s References ---- Barron's Regents Review Book, Physics. Chapter Two: Motion In One Dimension GBSSCI/PHYS/CLASS/1DKin/U1L1d.html Velocity and Speed phys-topic.cfm?Course=PHYS&TopicCode=01a Regents Questions Distance vs Displacement External Links ---- Mini Test- This is a helpful little quiz to furthur understand the difference between velocity and speed Velocity and Acceleration- If you feel you have learned enough about velocity check out acceleration!